The equation (REF ) is an important model of cardiac defibrillation [1]}, [2]}. In this model, \(I\)  is the extracellular stimulation current in the form \(I = \sum _{k=0}^{N} u_k(t) \chi _{\Omega _k}(x)\) , where \(\Omega _k(x)\)  are the characteristic functions of electrodes, and \(u_k\)  are the corresponding pulses. During defibrillation various regions of heart tissue are in different, usually random, phases of electrical activity (excited, refractory, partially recovered etc), and the purpose of defibrillation is to give an electric impulse that stimulates the entire heart and returns it to its normal (e.g. stationary) state. Therefore, understanding long time behavior of problems of type (REF ) is crucial in order to understand whether such recovery can take place, and how quickly it happens.
